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Evaluate the following limit : \(\lim\limits_{\text x \to 2}\cfrac{\sqrt{\text x^2+1}-\sqrt5}{\text x - 2}\)

lim(x→2) (√(x2 + 1)- √5)/(x - 2)

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Given \(\lim\limits_{\text x \to 2}\cfrac{\sqrt{\text x^2+1}-\sqrt5}{\text x - 2}\)

To find: the limit of the given equation when x tends to 2

Substituting x as 2, we get an indeterminant form of

Rationalizing the given equation

Formula: (a + b) (a - b) = a2 - b2

Now we can see that the indeterminant form is removed, so substituting x as 2

We get \(\lim\limits_{\text x \to 2}\cfrac{\sqrt{\text x^2+1}-\sqrt5}{\text x - 2}\) = \(\cfrac{2+2}{2\sqrt5}=\cfrac{2}{\sqrt5}\)

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